1. A New Technique for Destination Choice
TRB Planning Applications Conference
Houston May 2009
William G. Allen, Jr., P.E.
Transportation Consultant

2. Changes in Destination Choice
Old: gravity model New: logit model
Old: aggregate zone-zone totals New: individual tours
Old: both productions and attractions constrained New: only productions constrained
As part of the shift to tour-based models, destination choice models are changing
Almost all 4 step models use the gravity model to allocate trips between zones
Most tour-based models use a logit model to allocate individual trips
Mathematically, these approaches aren’t as different as you might think
One big difference between these 2 types of models is that in conventional models, both productions and attractions are constrained at the zone level
But in most tour-based models, attractions are not constrained

3. Distribution Functions
Gravity model
Logit model
For the record, here are the equations of the gravity and logit models
I show this slide to point out that both functions say kinda the same thing: that the trips from zone i to zone j are a function of the attractiveness of zone j relative to the attractiveness of all zones

4. Discrete Tour-Based Models
These are becoming popular
Operate on individual trips (tours)
Destination choice model creates tours
Each tour is modelled individually
Tour-based modeling is on the rise, as we all know
Biggest difference with the new models is that they operate on individual tours, not aggregate zone-to-zone movements

5. Discrete Destination Choice Models
Probability of trip from zone I going to zone J
Correct number of trips leaving zone I
Trips attracted to zone J may not match expectations
No attraction model
What if you want to estimate zonal attraction totals?
The new destination choice models estimate the number of trip productions in a zone, usually with a tour frequency model
Then they look at every individual origin and decide which destination zone it goes to
After all trips are allocated, these models do NOT check to see that the number of trips attracted to each zone matches the initially estimated attractions
This is because there ARE no initially estimated attractions
Most tour-based advocates defend this by saying that our attraction models aren’t very good anyway
But… what if you LIKE your attraction model, or for any reason, want to estimate a certain number of attractions in a zone?
You can’t do that with most, if not all, tour-based models because they’re singly-constrained

6. Travel Probability Gravity calculations are normally aggregate
But a gravity model can be applied in disaggregate fashion
Probability of trip from zone I going to zone J
Stochastic selection of attraction zone, similar to logit model
Another thing that is “given” in the new models is that the destinations MUST be allocated using a logit model
Maybe the logit model is superior for this purpose, but I haven’t seen anyone prove that yet
What if you have a gravity model that you happen to really like, or for some reason, just want to keep using?
Many people don’t realize that you can apply a gravity model to individual trips
Now I’m not saying this would definitely give better results than a logit model, I’m just saying it can be done

7. New Methodology Conventional model is applied stochastically
Use standard gravity formula to calculate probabilities
Calculate trips in random order by P zone
As trips are allocated, adjust attractions
So that’s really what this presentation is all about
I’m going to describe a way to use a doubly-constrained gravity function to allocate individual trips like a tour-based model
This slide basically explains how to do it
I’ll get into more details in a minute

8. Why do this? Maybe the attraction model is important
Check on production total
Jobs/housing balance
Permits comparison of aggregate vs. discrete procedures
Stepping stone towards advanced tour-based process
Speed up existing model with many zones
But first, we always have to have this slide: WHY?
I’m sure all the tour-based advocates out there are saying that right now: Why would you want to do this?
As I said, some planners LIKE having an attraction model and want their distribution process to match those numbers
Some planners LIKE their gravity model
This method could be used to do a pure comparison of conventional vs. the new procedures
For some, this could be a reasonable step towards a tour-based model
It is also a way to apply a conventional model differently, which could reduce running time and file size as you increase the number of zones in your area

9. Procedure Randomize production records by zone
For each record, gravity model calculates probability of travel to all zones
Allocate trip to destination zone J (Monte Carlo)
Decrease remaining attractions in J by 1
Repeat until all trips are allocated to destinations
So how does this procedure work?
Here’s the way I have implemented it – I’m sure there are other variations
The details are described in the paper
The first step is to put all production records in random order by production zone – you need to do this in order to avoid geographic bias
Then you use the gravity function to calculate the probability of travel to all zones
Then use those probabilities to allocate a trip to one attraction zone, using the same Monte Carlo method as in all tour-based models
Now, here’s the real secret to this process: you then reduce the number of attractions to the selected zone by 1, to make it slightly less attractive
Then repeat the same process until all trips are allocated
In this way you can match the initially estimated attractions in one pass – and don’t need multiple iterations

10. Software Conceptually simple, computationally not
Scripting in Cube possible, but run time is long
Faster in Fortran: 90 min to 13 min
It’s relatively simple in concept, but requires a LOT of calculations
I first wrote it in Cube, which was easy, but it ran a bit slowly
There may be a way to shorten it in Cube, I don’t know
I would guess it can be written using other software packages
For this project, I re-wrote it in Fortran, which reduced the running time by a factor of 7

11. Real World Example
Metropolitan Washington COG model of Commercial trips
Separate models for I/I and external trips
Simple trips, not tours
Balanced trip ends by zone (orig. = dest.)
1,972 real internal zones
Totals: 901K I/I, 63K external trips
To test the idea, I found a real-world example
The Washington area model of commercial trips
This is not necessarily the best type of trip for this test, but it was available
Washington area has almost 2000 zones
900,000 internal trips, 63,000 externals in 2005

12. Steps Normal trip generation
Create 1 prod. record per trip, in random zone order
Calculate Fij factors
Allocate each prod. record to attr. zone
Also run time of day in discrete fashion
Build trip tables from trip records
There was no change to conventional trip generation
A step was added to create 900,000 production records, in random order by origin zone
For each origin zone, run gravity model to get probability of trip going to each destination zone
For each production record, look at the probabilities and allocate the trip to a destination
Then go to the next record
After completing the destination model, run the time of day model in the same discrete fashion to allocate the trip to a time period

13. Results Conventional and new trip tables are very similar
Average trip lengths: old=25.87, new=25.96
Trip length distributions almost identical
COM VMT: old=10.8 M, new=11.5 M
Distribution takes longer, assignment is shorter
It’s easy to compare this new approach with the conventional approach
The average trip lengths almost the same
Trip length distributions are also nearly identical – they’re shown in the paper
Commercial trip VMT was a little higher
The time to run the new distribution model is higher but assignment takes less time – however, on balance, the run time increased overall

14. Conclusions “New” destination choice method developed
Destination choice step takes longer
Results comparable to conventional method
Easily expanded to other trip types
Applying an aggregate model this way is a stepping stone to a discrete tour-based model
I believe this is a fairly new technique – I couldn’t find anything similar in a literature search
With this method, it definitely takes longer to run trip distribution, compared to the conventional type of model, but I think all discrete methods have that problem
If you have a lot of zones, a discrete process may be more efficient for some things and may save running time in other steps
This is one of the few examples I’ve seen that compares a conventional aggregate approach to a tour-based discrete approach, using the same data – and the results are encouraging
This method may be something that encourages and facilitates the shift to a tour-based approach
Questions?